%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG037-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:04:45 PM UTC 2026
% Result : Unsatisfiable 15.81s 3.86s
% Output : CNFRefutation 15.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 47 ( 27 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] : product(X,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f55,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f60,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f73,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f74,plain,
product(a,b,d),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f75,plain,
product(a,additive_inverse(b),c),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
~ sum(c,d,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f77,plain,
~ sum(d,c,additive_identity),
inference(resolution,[status(thm)],[f76,f55]) ).
fof(f277,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X3,additive_identity)
| ~ sum(X1,X2,X3)
| ~ product(X0,X2,c)
| ~ product(X0,X1,d) ),
inference(resolution,[status(thm)],[f61,f77]) ).
fof(f1612,plain,
! [X0,X1] :
( ~ product(X0,additive_identity,additive_identity)
| ~ product(X0,additive_inverse(X1),c)
| ~ product(X0,X1,d) ),
inference(resolution,[status(thm)],[f277,f50]) ).
fof(f1632,plain,
! [X0,X1] :
( ~ product(X0,additive_inverse(X1),c)
| ~ product(X0,X1,d) ),
inference(forward_subsumption_resolution,[status(thm)],[f1612,f73]) ).
fof(f1723,plain,
~ product(a,b,d),
inference(resolution,[status(thm)],[f1632,f75]) ).
fof(f1731,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1723,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n001.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 04:20:29 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 15.81/3.86 % Refutation found
% 15.81/3.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 15.81/3.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.81/3.88 % Elapsed time: 3.412548 seconds
% 15.81/3.88 % CPU time: 26.499897 seconds
% 15.81/3.88 % Total memory used: 113.129 MB
% 15.81/3.88 % Net memory used: 100.176 MB
%------------------------------------------------------------------------------